If you guessed three then you're
wrong, in fact the number of strikeouts in an inning is limitless.

If first base is open or there are two outs and a
batter is struck out but the ball is not caught by the catcher the batter may
run to first base. He must be tagged out or thrown out to be out. If he is not
an out is not registered but the pitcher does get credit for a strikeout.

On October 4, 1888 Jon Andre of the New York Giants
faced this situation and recorded the first ever 4 strikeout inning, a feat
not that uncommon in baseball today.

There has never been a pitcher to record 5 strikeouts
in an inning in the majors but it has occurred on three occasions in the minor
leagues.